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Journal of Uncertain Systems 2025年第1期18卷

作者： Khatun, Jasminara Amanathulla, S. Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India Department of Mathematics Raghunathpur College Raghunathpur 723133 India

In real-life problems, information collected from multiple agents often exhibits "multipolar information," which cannot be accurately modeled by existing graph models. This paper introduces the m-polar picture fuzzy graph (mPPFG) as a more efficient model for such problems. The mPPFG offers a precise, flexible and comparable system compared to other graph models. The paper defines the mPPFG model and introduces new terms and properties such as order, degree, weighted arithmetic average (WAA) order, WAA degree, complement, homomorphism, isomorphism, eccentricity, radius, diameter and more. It also explores the concepts of m-polar antipodal picture fuzzy graphs, eccentric mPPFG, self-centered mPPFG and self-median mPPFG, highlighting their definitions and properties. The m-polar antipodal picture fuzzy graph represents a graph where each vertex is associated with an m-polar antipodal picture fuzzy set. The eccentric mPPFG focuses on highly eccentric vertices, while the self-centered mPPFG considers central vertices. The self-median mPPFG represents median vertices in the graph. The study of these graph types and their isomorphism properties contributes to a deeper understanding of the structural variations within mPPFGs. Furthermore, the paper proposes an application of the mPPFG model in evaluating the performance of ministers in India during their tenure. An algorithm is also developed for computing the performance of ministers. © 2024 World Scientific. All rights reserved.

关键词： complement diameter isomorphism m-polar antipodal PFG mPPFG Picture fuzzy graphs

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Multi-fuzzy complex nilpotent matrices

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International Journal of Fuzzy System Applications 2016年第4期5卷 52-76页

作者： Dey, Asit Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India

In this paper, the concept of multi-fuzzy matrix (MFM), multi-fuzzy complex matrix (MFCM), generalized multi-fuzzy complex matrix (GMFCM), generalized multi-fuzzy complex nilpotent matrix (GMFCNM) are introduced and have shown that the set of GMFCMs form a distributive lattice. Some properties and characterizations for GMFCNMs are established and in particular, a necessary and sufficient condition for an n × n GMFCNM to have the nilpotent index n is given. Finally, the reduction of GMFCNMs over a distributive lattice are given with some properties. © 2016, IGI Global.

关键词： Fuzzy Sets Generalized Multi-Fuzzy Complex Nilpotent Matrix Multi-Fuzzy Complex Matrix Multi-Fuzzy Matrix Nilpotent Matrix

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Multi-fuzzy complex numbers and multi-fuzzy complex sets

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International Journal of Fuzzy System Applications 2015年第2期4卷 15-27页

作者： Dey, Asit Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India

This paper presents a method to construct more general fuzzy complex numbers and sets from ordinary fuzzy complex numbers by introduced the ordered sequences of membership functions. It is concluded that multi fuzzy complex set is an extension of Buckley fuzzy complex set. Also, two types of multi-fuzzy complex numbers based on the forms z = x +iy and z = reiθ are investigated. Copyright © 2015, IGI Global.

关键词： Membership functions

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Application of (α,β)-soft intersectional sets on BCK/BCI-algebras

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International Journal of Intelligent Systems Technologies and Applications 2017年第3期16卷 269-288页

作者： Jana, Chiranjibe Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore721102 India

In this paper, the notion of (α,β)-soft intersectional set is introduced and explained with some examples. Then, some properties of (α,β)-soft intersectional BCK/BCI-algebras and (α,β)-soft intersectional BCK/BCI-ideals are investigated. Strong (α,β)- soft intersectional BCI-algebra is defined on the basis of BCI-subalgebras. The concept of an (α,β)-intersectional t-support of a soft set is introduced and proposed a condition for an (α,β)- intersectional t-support to be a soft BCK/BCI-subalgebras and soft ideal of a BCK/BCI-algebras. Also, it is shown that the image and inverse image of a BCK/BCI-algebras are also (α,β)-soft intersectional BCK/BCI-algebras. Again, (α,β)-soft intersectional BCK/BCI-ideal is developed on the basis of a homomorphism of BCK/BCI-algebras. Copyright © 2017 Inderscience Enterprises Ltd.

关键词： Algebra

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Shortest path problem on a network with imprecise edge weight

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Fuzzy Optimization and Decision Making 2005年第4期4卷 293-312页

作者： Nayeem, Sk.Md. Abu Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore-721 102 India

A network with its arc lengths as imprecise number, instead of a real number, namely, interval number and triangular fuzzy number is considered here. Existing ideas on addition and comparison between two imprecise numbers of same type are introduced. To obtain a fuzzy shortest path from a source vertex to all other vertices, a common algorithm is developed which works well on both types of imprecise numbers under consideration. In the proposed algorithm, a decision-maker is to negotiate with the obtained fuzzy shortest paths according to his/her view only when the means are same but the widths are different of the obtained paths. Otherwise, a fuzzy optimal path is obtained to which the decision-maker always satisfies with different grades of satisfaction. All pairs fuzzy shortest paths can be found by repeated use of the proposed algorithm. © 2005 Springer Science+Business Media, Inc.

关键词： Fuzzy sets

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Time variant multi-objective linear fractional interval-valued transportation problem

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applied mathematics(A Journal of Chinese Universities) 2022年第1期37卷 111-130页

作者： Dharmadas Mardanya Sankar Kumar Roy Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar UniversityMidnapore 721102West BengalIndia

This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.

关键词： fractional transportation problem multi-objective optimization interval number time variant parameter fuzzy programming Pareto optimal solution

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Analytics of an Imperfect Four-Layer Production Inventory Model Under Two-Level Credit Period Using Branch-and-Bound Technique

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Journal of the Operations Research Society of China 2022年第4期10卷 725-748页

作者： Subrata Panja Shyamal Kumar Mondal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar UniversityMidnaporeW.B.721102India

This paper explains an integrated production inventory supply chain model,which consists of a supplier,a manufacturer and a retailer under two-level credit *** is manufacturer’s credit period offered by the supplier,and other is retailer’s credit period offered by the ***,the manufacturer replenishes raw materials from the supplier and produces non-deteriorating products in some cycles of equal *** is noted that here four inventory structures have been considered to show the flow of the materials as either raw materials or finished products from supplier to retailer via *** in this model,manufacturer’s imperfect production has been *** imperfect items are not *** retailer receives good finished products from the manufacturer and sells these to his/her customers during some cycles of equal length in total time *** main objective is to find the optimal number of production and business cycles of the manufacturer such that the integrated system can get the maximum *** above discussed model is elaborated with the help of a numerical example,and a sensitivity analysis is done with respect to some parameters used in this model.

关键词： Supply chain Integrated production inventory Four-layer inventory system Imperfect production Two-level credit period

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Soft Matrix Game: A Hesitant Fuzzy MCDM Approach

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American Journal of Mathematical and Management Sciences 2021年第2期40卷 107-119页

作者： Jana, Jishu Kumar Roy, Sankar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University MidnaporeWest Bengal India

Soft set theory has emerged recently as a new mathematical tool to handle uncertainty. Sometimes decision makers are not sure about the decision-making criteria, where soft set theory provides an idea to deal with such uncertainties. Multi-criteria decision making (MCDM) involves choosing the best from several alternatives. MCDM methods such as TOPSIS and VIKOR depend on an aggregating function for presenting "closeness to the ideal" which arises due to the compromise solution. The VIKOR method of compromise ranking describes a compromise solution, providing a maximum for the "maximizing player" and minimum for the "opponent", which is an effective approach in an MCDM game. TOPSIS method presents a solution with the shortest distance to the positive ideal solution (PIS) and largest distance from the negative ideal solution (NIS). Also, hesitant fuzzy soft set is an appropriate tool to tackle the imprecise parameters introduced in MCDM problems by the decision maker (DM). In this paper, we extend the VIKOR and TOPSIS methods for solving MCDM game problems with hesitant fuzzy soft payoffs to determine the optimal strategies. Finally, a numerical example is incorporated to verify the extended VIKOR approach and the results are compared with those for the TOPSIS method. The paper ends with conclusions and outlooks. © 2020 Taylor & Francis Group, LLC.

关键词： Numerical methods

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Solving the shortest path problem with interval arcs

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Fuzzy Optimization and Decision Making 2006年第1期5卷 71-89页

作者： Sengupta, Atanu Pal, Tapan Kumar Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Medinipur - 721 102 India

This paper presents an algorithm for the shortest path problem when the connected arcs in a transportation network are represented as interval numbers. The methodology proposed in this paper considers fuzzy preference ordering of intervals (Sengupta and Pal (2000), European Journal of Operational Research 127, 28-43) from pessimistic and optimistic decision maker's point of view. © 2006 Springer Science+Business Media, Inc.

关键词： Algorithms

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Inventory of deteriorating complementary and substitute items with stock dependent demand

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American Journal of Mathematical and Management Sciences 2005年第1-2期25卷 83-96页

作者： Maity, K. Maiti, M. Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore - 721 102 India

The optimal production for an inventory control system of deteriorating multi-items where items are of complementary or substitute types is formulated with a resource constraint. Here, it is assumed that substitute products have linearly negative effect on one another's demands and this effect is positive for the complementary items. The effect of an item on the demand of the other item depends on the inventory level of the first item. The rate of deterioration of the items is stock dependent. An item's own demand is also stock dependent, shortages are not allowed, and deteriorated items are salvaged. The total profit which consists of the sales proceeds, production cost, inventory holding cost, salvage value is formulated as a Pontryagin Optimal Control problem for both steady and transient states and evaluated using optimal control theory satisfying the Generalized Legendre condition. The model is formulated in general form for n-items and in particular, is illustrated with two items for some numerical data. The optimum results are presented both in tabular form and graphically. Copyright © 2005 by American Sciences Press, Inc.

关键词： Inventory control

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